{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "13d83b59-57f7-48ee-8bff-deda7d28edc5",
   "metadata": {
    "tags": []
   },
   "source": [
    "\n",
    "# Max Colorable Induced Subgraph Problem\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a1e6d16-3076-4e94-a090-2ee17af45290",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Background\n",
    "\n",
    "Given a graph $G = (V,E)$ and number of colors K, find the **largest induced subgraph that can be colored using up to K colors**.\n",
    "\n",
    "A coloring is legal if:\n",
    "\n",
    "- each vetrex ${v_i}$ is assigned with a color $k_i \\in \\{0, 1, ..., k-1\\}$\n",
    "- adajecnt vertex have different colors: for each $v_i, v_j$ such that $(v_i, v_j) \\in E$, $k_i \\neq k_j$.\n",
    "\n",
    "An induced subgraph of a graph $G = (V,E)$ is a graph $G'=(V', E')$ such that $V'\\subset V$ and $E' = \\{(v_1, v_2) \\in E\\ |\\ v_1, v_2 \\in V'\\}$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bdc4e6a-199b-44b3-bd3f-fd24722b616b",
   "metadata": {},
   "source": [
    "## Define the optimization problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "83ddbd07-f7ab-4d80-b357-3890622d395f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:46.993834Z",
     "iopub.status.busy": "2024-05-07T15:59:46.993374Z",
     "iopub.status.idle": "2024-05-07T15:59:47.525960Z",
     "shell.execute_reply": "2024-05-07T15:59:47.525184Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import numpy as np\n",
    "import pyomo.environ as pyo\n",
    "\n",
    "\n",
    "def define_max_k_colorable_model(graph, K):\n",
    "    model = pyo.ConcreteModel()\n",
    "\n",
    "    nodes = list(graph.nodes())\n",
    "    colors = range(0, K)\n",
    "\n",
    "    # each x_i states if node i belongs to the cliques\n",
    "    model.x = pyo.Var(colors, nodes, domain=pyo.Binary)\n",
    "    x_variables = np.array(list(model.x.values()))\n",
    "\n",
    "    adjacency_matrix = nx.convert_matrix.to_numpy_array(graph, nonedge=0)\n",
    "    adjacency_matrix_block_diagonal = np.kron(np.eye(K), adjacency_matrix)\n",
    "\n",
    "    # constraint that 2 nodes sharing an edge mustn't have the same color\n",
    "    model.conflicting_color_constraint = pyo.Constraint(\n",
    "        expr=x_variables @ adjacency_matrix_block_diagonal @ x_variables == 0\n",
    "    )\n",
    "\n",
    "    # each node should be colored\n",
    "    @model.Constraint(nodes)\n",
    "    def each_node_is_colored_once_or_zero(model, node):\n",
    "        return sum(model.x[color, node] for color in colors) <= 1\n",
    "\n",
    "    def is_node_colored(node):\n",
    "        is_colored = np.prod([(1 - model.x[color, node]) for color in colors])\n",
    "        return 1 - is_colored\n",
    "\n",
    "    # maximize the number of nodes in the chosen clique\n",
    "    model.value = pyo.Objective(\n",
    "        expr=sum(is_node_colored(node) for node in nodes), sense=pyo.maximize\n",
    "    )\n",
    "\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3496c5d6-7df6-49fb-b5b9-5ba48d2b7d62",
   "metadata": {},
   "source": [
    "### Initialize the model with parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bc9871c1-224e-4206-b39e-af7e448aca70",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:47.531914Z",
     "iopub.status.busy": "2024-05-07T15:59:47.530379Z",
     "iopub.status.idle": "2024-05-07T15:59:48.475400Z",
     "shell.execute_reply": "2024-05-07T15:59:48.474677Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph = nx.erdos_renyi_graph(6, 0.5, seed=7)\n",
    "nx.draw_kamada_kawai(graph, with_labels=True)\n",
    "\n",
    "NUM_COLORS = 2\n",
    "\n",
    "coloring_model = define_max_k_colorable_model(graph, NUM_COLORS)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "958deac9-b057-485e-bea0-52b95664ae6b",
   "metadata": {},
   "source": [
    "### print the resulting pyomo model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e5ba50c9-5d89-4ebf-9475-830da3ce5539",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:48.480486Z",
     "iopub.status.busy": "2024-05-07T15:59:48.479062Z",
     "iopub.status.idle": "2024-05-07T15:59:48.490131Z",
     "shell.execute_reply": "2024-05-07T15:59:48.489448Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4 Set Declarations\n",
      "    each_node_is_colored_once_or_zero_index : Size=1, Index=None, Ordered=Insertion\n",
      "        Key  : Dimen : Domain : Size : Members\n",
      "        None :     1 :    Any :    6 : {0, 1, 2, 3, 4, 5}\n",
      "    x_index : Size=1, Index=None, Ordered=True\n",
      "        Key  : Dimen : Domain              : Size : Members\n",
      "        None :     2 : x_index_0*x_index_1 :   12 : {(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5)}\n",
      "    x_index_0 : Size=1, Index=None, Ordered=Insertion\n",
      "        Key  : Dimen : Domain : Size : Members\n",
      "        None :     1 :    Any :    2 : {0, 1}\n",
      "    x_index_1 : Size=1, Index=None, Ordered=Insertion\n",
      "        Key  : Dimen : Domain : Size : Members\n",
      "        None :     1 :    Any :    6 : {0, 1, 2, 3, 4, 5}\n",
      "\n",
      "1 Var Declarations\n",
      "    x : Size=12, Index=x_index\n",
      "        Key    : Lower : Value : Upper : Fixed : Stale : Domain\n",
      "        (0, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "        (0, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "        (0, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "        (0, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "        (0, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "        (0, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "\n",
      "1 Objective Declarations\n",
      "    value : Size=1, Index=None, Active=True\n",
      "        Key  : Active : Sense    : Expression\n",
      "        None :   True : maximize : 1 - (1 - x[0,0])*(1 - x[1,0]) + 1 - (1 - x[0,1])*(1 - x[1,1]) + 1 - (1 - x[0,2])*(1 - x[1,2]) + 1 - (1 - x[0,3])*(1 - x[1,3]) + 1 - (1 - x[0,4])*(1 - x[1,4]) + 1 - (1 - x[0,5])*(1 - x[1,5])\n",
      "\n",
      "2 Constraint Declarations\n",
      "    conflicting_color_constraint : Size=1, Index=None, Active=True\n",
      "        Key  : Lower : Body                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  : Upper : Active\n",
      "        None :   0.0 : (x[0,1] + x[0,2] + x[0,4])*x[0,0] + (x[0,0] + x[0,2] + x[0,3] + x[0,5])*x[0,1] + (x[0,0] + x[0,1] + x[0,3] + x[0,4] + x[0,5])*x[0,2] + (x[0,1] + x[0,2] + x[0,4])*x[0,3] + (x[0,0] + x[0,2] + x[0,3] + x[0,5])*x[0,4] + (x[0,1] + x[0,2] + x[0,4])*x[0,5] + (x[1,1] + x[1,2] + x[1,4])*x[1,0] + (x[1,0] + x[1,2] + x[1,3] + x[1,5])*x[1,1] + (x[1,0] + x[1,1] + x[1,3] + x[1,4] + x[1,5])*x[1,2] + (x[1,1] + x[1,2] + x[1,4])*x[1,3] + (x[1,0] + x[1,2] + x[1,3] + x[1,5])*x[1,4] + (x[1,1] + x[1,2] + x[1,4])*x[1,5] :   0.0 :   True\n",
      "    each_node_is_colored_once_or_zero : Size=6, Index=each_node_is_colored_once_or_zero_index, Active=True\n",
      "        Key : Lower : Body            : Upper : Active\n",
      "          0 :  -Inf : x[0,0] + x[1,0] :   1.0 :   True\n",
      "          1 :  -Inf : x[0,1] + x[1,1] :   1.0 :   True\n",
      "          2 :  -Inf : x[0,2] + x[1,2] :   1.0 :   True\n",
      "          3 :  -Inf : x[0,3] + x[1,3] :   1.0 :   True\n",
      "          4 :  -Inf : x[0,4] + x[1,4] :   1.0 :   True\n",
      "          5 :  -Inf : x[0,5] + x[1,5] :   1.0 :   True\n",
      "\n",
      "8 Declarations: x_index_0 x_index_1 x_index x conflicting_color_constraint each_node_is_colored_once_or_zero_index each_node_is_colored_once_or_zero value\n"
     ]
    }
   ],
   "source": [
    "coloring_model.pprint()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a108c16-e77f-4dc5-89f1-4cbbed06bff5",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Setting Up the Classiq Problem Instance\n",
    "\n",
    "In order to solve the Pyomo model defined above, we use the Classiq combinatorial optimization engine. For the quantum part of the QAOA algorithm (`QAOAConfig`) - define the number of repetitions (`num_layers`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6d1db79c-4d99-49a8-9347-5d6ad67353e3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:48.494703Z",
     "iopub.status.busy": "2024-05-07T15:59:48.493521Z",
     "iopub.status.idle": "2024-05-07T15:59:50.391512Z",
     "shell.execute_reply": "2024-05-07T15:59:50.390855Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from classiq import construct_combinatorial_optimization_model\n",
    "from classiq.applications.combinatorial_optimization import OptimizerConfig, QAOAConfig\n",
    "\n",
    "qaoa_config = QAOAConfig(num_layers=8)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ed22929-18cf-47e6-9c2a-ad635365a48a",
   "metadata": {},
   "source": [
    "For the classical optimization part of the QAOA algorithm we define the maximum number of classical iterations (`max_iteration`) and the $\\alpha$-parameter (`alpha_cvar`) for running CVaR-QAOA, an improved variation of the QAOA algorithm [[3](#cvar)]:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "13247459-f1c8-48cf-83f0-f13eb66365ca",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:50.394696Z",
     "iopub.status.busy": "2024-05-07T15:59:50.394038Z",
     "iopub.status.idle": "2024-05-07T15:59:50.398249Z",
     "shell.execute_reply": "2024-05-07T15:59:50.397671Z"
    },
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "optimizer_config = OptimizerConfig(max_iteration=20, alpha_cvar=0.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31c98d00-ed27-4eb9-86c3-580825ac9677",
   "metadata": {},
   "source": [
    "Lastly, we load the model, based on the problem and algorithm parameters, which we can use to solve the problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "46f35710-d7b3-49d0-ae25-5e36f1f6dd95",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:50.400620Z",
     "iopub.status.busy": "2024-05-07T15:59:50.400214Z",
     "iopub.status.idle": "2024-05-07T15:59:54.059295Z",
     "shell.execute_reply": "2024-05-07T15:59:54.058630Z"
    },
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "qmod = construct_combinatorial_optimization_model(\n",
    "    pyo_model=coloring_model,\n",
    "    qaoa_config=qaoa_config,\n",
    "    optimizer_config=optimizer_config,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "011b8c25-00b5-4099-9079-eb46f640343d",
   "metadata": {},
   "source": [
    "We also set the quantum backend we want to execute on:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c87b4cd7-a780-4d78-8335-f78b38584d80",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:54.062409Z",
     "iopub.status.busy": "2024-05-07T15:59:54.062022Z",
     "iopub.status.idle": "2024-05-07T15:59:54.196397Z",
     "shell.execute_reply": "2024-05-07T15:59:54.195183Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from classiq import set_execution_preferences\n",
    "from classiq.execution import ClassiqBackendPreferences, ExecutionPreferences\n",
    "\n",
    "backend_preferences = ExecutionPreferences(\n",
    "    backend_preferences=ClassiqBackendPreferences(backend_name=\"aer_simulator\")\n",
    ")\n",
    "\n",
    "qmod = set_execution_preferences(qmod, backend_preferences)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "96507f00-8d76-4ca3-b0dd-0b20d44c1e80",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:54.211269Z",
     "iopub.status.busy": "2024-05-07T15:59:54.209802Z",
     "iopub.status.idle": "2024-05-07T15:59:54.709502Z",
     "shell.execute_reply": "2024-05-07T15:59:54.708816Z"
    }
   },
   "outputs": [],
   "source": [
    "from classiq import write_qmod\n",
    "\n",
    "write_qmod(qmod, \"max_induced_k_color_subgraph\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e63e8272-cfd5-4a7d-9ce9-73486dab643a",
   "metadata": {},
   "source": [
    "## Synthesizing the QAOA Circuit and Solving the Problem\n",
    "\n",
    "We can now synthesize and view the QAOA circuit (ansatz) used to solve the optimization problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1b3e64a1-eae5-4ffc-9a08-1d5131401422",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:54.712426Z",
     "iopub.status.busy": "2024-05-07T15:59:54.711967Z",
     "iopub.status.idle": "2024-05-07T16:01:10.648412Z",
     "shell.execute_reply": "2024-05-07T16:01:10.647712Z"
    },
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Opening: https://platform.classiq.io/circuit/941213ad-27c1-464a-8fb9-3936559e6168?version=0.41.0.dev39%2B79c8fd0855\n"
     ]
    }
   ],
   "source": [
    "from classiq import show, synthesize\n",
    "\n",
    "qprog = synthesize(qmod)\n",
    "show(qprog)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e99f6361-a9ac-48d1-a7b1-c77a0f09adfe",
   "metadata": {},
   "source": [
    "We now solve the problem by calling the `execute` function on the quantum program we have generated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d7520962-de83-42de-928b-34e72cc01caf",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T16:01:10.651764Z",
     "iopub.status.busy": "2024-05-07T16:01:10.651358Z",
     "iopub.status.idle": "2024-05-07T16:02:57.582923Z",
     "shell.execute_reply": "2024-05-07T16:02:57.582238Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from classiq import execute\n",
    "\n",
    "res = execute(qprog).result()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56a8d4c5-4f22-4107-999f-2eaa147e52d1",
   "metadata": {},
   "source": [
    "We can check the convergence of the run:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "58e49053-f2c6-40f9-9865-9f9e79df6eeb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T16:02:57.586876Z",
     "iopub.status.busy": "2024-05-07T16:02:57.586610Z",
     "iopub.status.idle": "2024-05-07T16:02:57.617957Z",
     "shell.execute_reply": "2024-05-07T16:02:57.617181Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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",
      "text/plain": [
       "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=640x480>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from classiq.execution import VQESolverResult\n",
    "\n",
    "vqe_result = res[0].value\n",
    "vqe_result.convergence_graph"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ccd880e2-9dd0-44c2-8d9e-1d892ed5faec",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Optimization Results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6716ab8d-ed59-49ce-a866-b0d344c421dd",
   "metadata": {},
   "source": [
    "We can also examine the statistics of the algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1631190c-308e-4300-9984-021fef022f2d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T16:02:57.622149Z",
     "iopub.status.busy": "2024-05-07T16:02:57.621887Z",
     "iopub.status.idle": "2024-05-07T16:02:58.754711Z",
     "shell.execute_reply": "2024-05-07T16:02:58.753952Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probability</th>\n",
       "      <th>cost</th>\n",
       "      <th>solution</th>\n",
       "      <th>count</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>401</th>\n",
       "      <td>0.001</td>\n",
       "      <td>5.0</td>\n",
       "      <td>[1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0]</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>572</th>\n",
       "      <td>0.001</td>\n",
       "      <td>4.0</td>\n",
       "      <td>[1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0]</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>334</th>\n",
       "      <td>0.001</td>\n",
       "      <td>3.0</td>\n",
       "      <td>[1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0]</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>222</th>\n",
       "      <td>0.001</td>\n",
       "      <td>3.0</td>\n",
       "      <td>[0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1]</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>169</th>\n",
       "      <td>0.001</td>\n",
       "      <td>3.0</td>\n",
       "      <td>[0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0]</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     probability  cost                              solution  count\n",
       "401        0.001   5.0  [1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0]      1\n",
       "572        0.001   4.0  [1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0]      1\n",
       "334        0.001   3.0  [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0]      1\n",
       "222        0.001   3.0  [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1]      1\n",
       "169        0.001   3.0  [0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0]      1"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "from classiq.applications.combinatorial_optimization import (\n",
    "    get_optimization_solution_from_pyo,\n",
    ")\n",
    "\n",
    "solution = get_optimization_solution_from_pyo(\n",
    "    coloring_model, vqe_result=vqe_result, penalty_energy=qaoa_config.penalty_energy\n",
    ")\n",
    "optimization_result = pd.DataFrame.from_records(solution)\n",
    "optimization_result.sort_values(by=\"cost\", ascending=False).head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1de0dda7-16f4-40a8-91f6-d65eb9e73565",
   "metadata": {},
   "source": [
    "And the histogram:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f57b11fe-d3de-4226-9b1e-f2d82ccb51ef",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T16:02:58.759575Z",
     "iopub.status.busy": "2024-05-07T16:02:58.758336Z",
     "iopub.status.idle": "2024-05-07T16:02:59.110565Z",
     "shell.execute_reply": "2024-05-07T16:02:59.109232Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<Axes: title={'center': 'cost'}>]], dtype=object)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "optimization_result.hist(\"cost\", weights=optimization_result[\"probability\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a1aff9e-e2a2-4ce1-b882-362ce6502736",
   "metadata": {},
   "source": [
    "Let us plot the best solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b8994248-1c5a-4959-8845-e325755833d4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T16:02:59.115579Z",
     "iopub.status.busy": "2024-05-07T16:02:59.114407Z",
     "iopub.status.idle": "2024-05-07T16:02:59.353197Z",
     "shell.execute_reply": "2024-05-07T16:02:59.352509Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "best_solution = optimization_result.solution[optimization_result.cost.idxmax()]\n",
    "\n",
    "one_hot_solution = np.array(best_solution).reshape([NUM_COLORS, len(graph.nodes)])\n",
    "integer_solution = np.argmax(one_hot_solution, axis=0)\n",
    "\n",
    "colored_nodes = np.array(graph.nodes)[one_hot_solution.sum(axis=0) != 0]\n",
    "colors = integer_solution[colored_nodes]\n",
    "\n",
    "pos = nx.kamada_kawai_layout(graph)\n",
    "nx.draw(graph, pos=pos, with_labels=True, alpha=0.3, node_color=\"k\")\n",
    "nx.draw(graph.subgraph(colored_nodes), pos=pos, node_color=colors, cmap=plt.cm.rainbow)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2333c7d2-cf8c-46db-a9b5-23802a54f395",
   "metadata": {},
   "source": [
    "## Classical optimizer results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a280c3a8-4dbe-420f-9bdd-da2d34ddae4d",
   "metadata": {},
   "source": [
    "Lastly, we can compare to the classical solution of the problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "73d2b211-52e7-4c29-9c46-8153129aba79",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T16:02:59.358007Z",
     "iopub.status.busy": "2024-05-07T16:02:59.356906Z",
     "iopub.status.idle": "2024-05-07T16:02:59.537763Z",
     "shell.execute_reply": "2024-05-07T16:02:59.537165Z"
    },
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ERROR: Solver (asl) returned non-zero return code (-6)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ERROR: Solver log: Couenne 0.5.8 -- an Open-Source solver for Mixed Integer\n",
      "    Nonlinear Optimization Mailing list: couenne@list.coin-or.org\n",
      "    Instructions: http://www.coin-or.org/Couenne malloc_consolidate(): invalid\n",
      "    chunk size couenne:\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solver might have not exited normally. Try again\n",
      "Model unknown\n",
      "\n",
      "  Variables:\n",
      "    x : Size=12, Index=x_index\n",
      "        Key    : Lower : Value : Upper : Fixed : Stale : Domain\n",
      "        (0, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "        (0, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "        (0, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "        (0, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "        (0, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "        (0, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "\n",
      "  Objectives:\n",
      "    value : Size=1, Index=None, Active=True\n",
      "ERROR: evaluating object as numeric value: x[0,0]\n",
      "        (object: <class 'pyomo.core.base.var._GeneralVarData'>)\n",
      "    No value for uninitialized NumericValue object x[0,0]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ERROR: evaluating object as numeric value: value\n",
      "        (object: <class 'pyomo.core.base.objective.ScalarObjective'>)\n",
      "    No value for uninitialized NumericValue object x[0,0]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        Key : Active : Value\n",
      "        None :   None :  None\n",
      "\n",
      "  Constraints:\n",
      "    conflicting_color_constraint : Size=1\n",
      "        Key  : Lower : Body : Upper\n",
      "        None :   0.0 : None :   0.0\n",
      "    each_node_is_colored_once_or_zero : Size=6\n",
      "        Key : Lower : Body : Upper\n",
      "          0 :  None : None :   1.0\n",
      "          1 :  None : None :   1.0\n",
      "          2 :  None : None :   1.0\n",
      "          3 :  None : None :   1.0\n",
      "          4 :  None : None :   1.0\n",
      "          5 :  None : None :   1.0\n"
     ]
    }
   ],
   "source": [
    "from pyomo.common.errors import ApplicationError\n",
    "from pyomo.opt import SolverFactory\n",
    "\n",
    "solver = SolverFactory(\"couenne\")\n",
    "result = None\n",
    "try:\n",
    "    result = solver.solve(coloring_model)\n",
    "except ApplicationError:\n",
    "    print(\"Solver might have not exited normally. Try again\")\n",
    "\n",
    "coloring_model.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c4a11618-40ae-4174-b296-a37afa65adce",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T16:02:59.552664Z",
     "iopub.status.busy": "2024-05-07T16:02:59.552129Z",
     "iopub.status.idle": "2024-05-07T16:02:59.564143Z",
     "shell.execute_reply": "2024-05-07T16:02:59.563341Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "if result:\n",
    "    classical_solution = [\n",
    "        pyo.value(coloring_model.x[i, j])\n",
    "        for i in range(NUM_COLORS)\n",
    "        for j in range(len(graph.nodes))\n",
    "    ]\n",
    "    one_hot_solution = np.array(classical_solution).reshape(\n",
    "        [NUM_COLORS, len(graph.nodes)]\n",
    "    )\n",
    "    integer_solution = np.argmax(one_hot_solution, axis=0)\n",
    "\n",
    "    colored_nodes = np.array(graph.nodes)[one_hot_solution.sum(axis=0) != 0]\n",
    "    colors = integer_solution[colored_nodes]\n",
    "\n",
    "    pos = nx.kamada_kawai_layout(graph)\n",
    "    nx.draw(graph, pos=pos, with_labels=True, alpha=0.3, node_color=\"k\")\n",
    "    nx.draw(\n",
    "        graph.subgraph(colored_nodes), pos=pos, node_color=colors, cmap=plt.cm.rainbow\n",
    "    )"
   ]
  }
 ],
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